Ermakov–Ray–Reid Systems in (2+1)-Dimensional Rotating Shallow Water Theory


Address for correspondence: C. Rogers, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, HK; e-mail:


A (2+1)-dimensional rotating shallow water system with an underlying circular paraboloidal bottom topography is shown to admit a multiparameter integrable nonlinear subsystem of Ermakov–Ray–Reid type. The latter system, which describes the time evolution of the semi-axes of the elliptical moving shoreline on the paraboidal basin, is also Hamiltonian. The complete solution of the generic eight-dimensional dynamical system governing the reduction is obtained in terms of an elliptic integral representation.